Space of modular forms of level 345 and weight 2

• Label: 345.2
• Level: 345
• Weight: 2
• Dimension: 2771
• Nonzero newspaces: 12
• Newform subspaces: 35
• Sturm bound: 16896
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 35 \)
Sturm bound:			\(16896\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(345))\).

	Total	New	Old
Modular forms	4576	3019	1557
Cusp forms	3873	2771	1102
Eisenstein series	703	248	455

Trace form

2771 * q + 5 * q^2 - 19 * q^3 - 35 * q^4 - q^5 - 65 * q^6 - 36 * q^7 + 9 * q^8 - 23 * q^9 - 61 * q^10 + 20 * q^11 - 17 * q^12 - 26 * q^13 + 24 * q^14 - 41 * q^15 - 187 * q^16 - 30 * q^17 - 105 * q^18 - 76 * q^19 - 79 * q^20 - 124 * q^21 - 148 * q^22 - 65 * q^23 - 155 * q^24 - 111 * q^25 - 50 * q^26 - 85 * q^27 - 164 * q^28 - 10 * q^29 - 76 * q^30 - 144 * q^31 - 15 * q^32 - 40 * q^33 - 74 * q^34 - 36 * q^35 - 101 * q^36 - 162 * q^37 - 152 * q^38 - 100 * q^39 - 233 * q^40 - 66 * q^41 - 218 * q^42 - 184 * q^43 - 232 * q^44 - 45 * q^45 - 415 * q^46 - 144 * q^47 - 213 * q^48 - 237 * q^49 - 39 * q^50 - 132 * q^51 - 390 * q^52 - 14 * q^53 - 21 * q^54 - 134 * q^55 - 100 * q^56 - 16 * q^57 - 178 * q^58 - 20 * q^59 + 60 * q^60 - 66 * q^61 + 96 * q^62 + 96 * q^63 + 69 * q^64 + 18 * q^65 + 88 * q^66 + 130 * q^68 + 111 * q^69 - 108 * q^70 + 88 * q^71 + 251 * q^72 + 10 * q^73 + 50 * q^74 + 3 * q^75 - 204 * q^76 - 80 * q^77 - 64 * q^78 - 140 * q^79 - 165 * q^80 - 243 * q^81 - 162 * q^82 - 116 * q^83 - 142 * q^84 - 272 * q^85 - 300 * q^86 - 260 * q^87 - 16 * q^88 - 162 * q^89 - 215 * q^90 - 416 * q^91 - 235 * q^92 - 276 * q^93 - 368 * q^94 - 98 * q^95 - 255 * q^96 - 82 * q^97 - 19 * q^98 - 222 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
345.2.a	\(\chi_{345}(1, \cdot)\)	345.2.a.a	1	1
		345.2.a.b	1
		345.2.a.c	1
		345.2.a.d	1
		345.2.a.e	1
		345.2.a.f	1
		345.2.a.g	2
		345.2.a.h	2
		345.2.a.i	2
		345.2.a.j	3
345.2.b	\(\chi_{345}(139, \cdot)\)	345.2.b.a	2	1
		345.2.b.b	2
		345.2.b.c	6
		345.2.b.d	14
345.2.c	\(\chi_{345}(206, \cdot)\)	345.2.c.a	16	1
		345.2.c.b	16
345.2.h	\(\chi_{345}(344, \cdot)\)	345.2.h.a	4	1
		345.2.h.b	8
		345.2.h.c	8
		345.2.h.d	24
345.2.i	\(\chi_{345}(47, \cdot)\)	345.2.i.a	4	2
		345.2.i.b	4
		345.2.i.c	80
345.2.j	\(\chi_{345}(22, \cdot)\)	345.2.j.a	48	2
345.2.m	\(\chi_{345}(16, \cdot)\)	345.2.m.a	30	10
		345.2.m.b	30
		345.2.m.c	50
		345.2.m.d	50
345.2.n	\(\chi_{345}(14, \cdot)\)	345.2.n.a	40	10
		345.2.n.b	400
345.2.s	\(\chi_{345}(11, \cdot)\)	345.2.s.a	160	10
		345.2.s.b	160
345.2.t	\(\chi_{345}(4, \cdot)\)	345.2.t.a	240	10
345.2.w	\(\chi_{345}(7, \cdot)\)	345.2.w.a	480	20
345.2.x	\(\chi_{345}(2, \cdot)\)	345.2.x.a	880	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(345))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(345)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)